Parallel imaging with multiple receivers is employed in known Magnetic Resonance Imaging (MRI) systems that are used both clinically and in basic science research. GRAPPA (generalized auto-calibrating partially parallel acquisitions) based reconstructions fill in missing k-space data using a local weighted average of neighboring k-space signals acquired by multiple receiver elements. K-space is the temporary image space in which data from digitized MR signals is stored during data acquisition and comprises raw data in a spatial frequency domain before reconstruction. When k-space is full (at the end of an MR scan), the data is mathematically processed to produce a final image. Given a limited set of auto-calibration data, the number of parameters to fit can rapidly approach the same order as the number of equations determined by the number of calibration data points. Over-fitting the calibration data makes the result sensitive to noise and unstable. At the opposite extreme under-fitting the data also results in poor image reconstruction and residual aliasing artifacts. Both issues become more sensitive with high reduction factors, limited calibration data or high-channel coil arrays. A parsimonious choice of reconstruction kernel minimizes residual fitting error of the model while simultaneously penalizing over-complex models. Known systems fail to comprehensively extend the kernel resulting in less than optimal MR image reconstruction. A system according to invention principles addresses these deficiencies and related problems.